Complementation of the subspace of radial multipliers in the space of Fourier multipliers on $\mathbb{R}^n$
Compl\'ementation du sous-espace des multiplicateurs radiaux dans l'espace des multiplicateurs de Fourier sur $\mathbb{R}^n$
Abstract
In this short note, we prove that the subspace of radial multipliers is contractively complemented in the space of Fourier multipliers on the Bochner space $\mathrm{L}^p(\mathbb{R}^n,X)$ where $X$ is a Banach space and where $1 \leq p <\infty$. Moreover, if $X = \mathbb{C}$, then this complementation preserves the positivity of multipliers.
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